Prosthetic devices are often implanted using sutures. For example, prosthetic heart valves and annuloplasty rings can be secured to a native heart valve annulus using sutures. Conventionally, the loose ends of the sutures are tied in knots to secure them together and/or to secure the prosthetic device to the adjacent tissue. However, the process of tying knots in sutures can be time consuming and difficult, the amount of slack left in the sutures can be difficult to control, the knots can be difficult or impossible to untie, and/or the knots can accidentally come loose. Thus, there is a need in the art for ways to secure prosthetic devices using sutures but without tying knots in the sutures.